Hoyle's Calculation of the Odds of Life

This web page addresses probably one of the most quoted statements about
evolution -- that the odds of life arising by chance are 1 in
1040,000. Hoping to find the basis of this computation, I decided
to track down the reference. Unfortunately, what I found was not a series of
probabalistic equations, but rather an account of Hoyle saying that he
computed this number. As far as I can tell, there is no publicly available
documentation supporting this figure. (I haven't checked out his books yet.
It may be in there.)

Abiogenesis is a mathematical impossibility. Sir Fred Hoyle, a British
astronomer and mathematician, calculated the odds of one simple bacterium
arising from a primordial soup. He assumed that the 20 amino acids were
present in the soup (contrary to the results of the Miller-Urey experiment,
which yielded only seven of the simplest amino acids).
A simple bacterium is comprised of 2,000 different functioning proteins. In
turn, each protein consists of a chain of about 300 amino acids. There are 20
distinct amino acids, so the odds of one proteinated amino acid occurring in
the correct sequence is one in 20. The odds of 300 occurring in the correct
sequence is one in 30020. Hoyle realized that there can be some
variation in the exact sequence, so the odds would be reduced to one in
1020. But because there must be 2,000 different functioning
proteins, the odds of the spontaneous generation of a cell is one in
10(20)(2,000) = 1040,000.
Even ignoring the problems beyond the math (such as the counter-productive
effects that individual essential chemical components have upon each other,
and the inability to create all 20 amino acids under simulated conditions),
abiogenesis is impossible.

It should be stated that biological evolution has very little to do with
abiogenesis. The former describes the gradual change in the gene pool of a
species, while the latter addresses the creation of life from non-living
matter.

That said, there are several problems with this analysis:

Further, Hoyle's calculations, as described by many Christians, assume
that the combinations are independent events, which is not generally the case
with molecular interactions. Lastly, it is not valid to apply probability to an
event that has already occurred -- it's like saying that the odds of winning
the lottery are 1 in 23 million, so no one could have won it.

The analysis assumes independence of variables (proteins, molecules,
etc.) This is obviously false, as we know that proteins strongly interact.
This means that certain combinations will not occur because the interactions
disallow them. If one takes dependence into account, the numbers will be
lower.

The analysis assumes independence of trials. That is, it assumes that one
combination is created, evaluated, then destroyed. In fact, the combinations
interact strongly with each other---groups of proteins interact with other
groups of proteins. As a result, the analysis is flawed.

Even if we believe the independence argument, we have no
data on how many trials there have been. In the lottery, we know that someone
will win because we know that even though the odds are astronomical of
winning, there are many tickets sold. When it comes to life, we have no
idea how many "losing tickets" there are. So any number is meaningless
unless we have the context for interpreting it.

Below is the article that appeared in the November 12, 1981 issue of
Nature, page 105 (volume 294, number 5837). It is a text box in the
"News" section of the journal.

Hoyle on Evolution

The serious part of the Kellogg symposium provided Sir Fred Hoyle with an
opportunity for a moderate (and self-critical) statement of his case for
disbelieving conventional views about the evolution of the Universe, the "big
bang" among them. Hoyle has been associated with the Kellogg laboratory since
his collaboration in the mid-195Os with W.A. Fowler and the two Burbidges
(Margaret and Geoffrey), now known as the gang of four, on the problem of
nucleogenesis.

Hoyle said last week that, although content in the mid-1960s to give the
supposed connection between the microwave background radiation and the big bang
a "good run for its money", he had now lost patience with this approach. Two of
his reasons involve the origin of life -- the calculated time since the origin
of the Universe of 10,000 million years or so is not enough to account for the
evolution of living forms, while adiabatic expansion of the Universe would have
been inimical to the evolution of highly ordered forms. But Hoyle also said
that new evidence in support of the big-bang hypothesis was emerging only
slowly. Yet "when people are on the right track, I new facts emerge quickly".
Hoyle said he would change his view if it turned out that neutrinos have a mass
of between 20 and 30 electron volts.

The essence of his argument last week was that the information content of the
higher forms of life is represented by the number 1040,000 --
representing the specificity with which some 2,000 genes, each of which might
be chosen from 1020 nucleotide sequences of the appropriate length,
might be defined. Evolutionary processes would, Hoyle said, require several
Hubble times to yield such a result. The chance that higher life forms might
have emerged in this way is comparable with the chance that "a tornado sweeping
through a junk-yard might assemble a Boeing 747 from the materials therein".

Hoyle acknowledged that steady-state theories of cosmologies, of which he was
one of the chief exponents in the 1950s, are not now tenable because of the
evidence for evolutionary galactic and stellar processes. But the big-bang view
is similarly not tenable because of the way in which it implies the degradation
of information. Of adherents of biological evolution, Hoyle said he was at a
loss to understand "biologists' widespread compulsion to deny what seems to me
to be obvious".